In accordance with the Remainder theorem, it is enough to check if
(1) the number -2 is the root of the first polynomial:
indeed, = -32 + 32 = 0;
so, -2 is the root; hence the polynomial is divisible by (x+2).
(2) the number is the root of the second polynomial:
indeed, - = - = 0;
so, is the root; hence the polynomial is divisible by .
The ANSWER is "YES" in both cases.
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Theorem (the remainder theorem)
1. The remainder of division the polynomial by the binomial is equal to the value of the polynomial.
2. The binomial divides the polynomial if and only if the value of is the root of the polynomial , i.e. .
3. The binomial factors the polynomial if and only if the value of is the root of the polynomial , i.e. .
